Variation talk: Articulating meaning in statistics

Little is known about the way that teachers articulate notions of variation in their own words. The study reported here was conducted with 17 prospective secondary math and science teachers enrolled in a preservice teacher education course which engaged them in statistical inquiry of testing data. This qualitative study examines how these preservice teachers articulated notions of variation as they compared two distributions. Although the teachers made use of tandard statistical language, they also expressed rich views of variation through nonstandard terminology. This paper details the statistical language used by the rospective teachers, categorizing both standard and nonstandard expressions. Their nonstandard language revealed strong relationships between expressions of variation and expressions of distribution. Implications and the benefits of nonstandard language in statistics are outlined.

Using distributions as statistical evidence in well-structured and ill-structured problems

Research has suggested that understanding in well-structured settings often does not transfer to the everyday, less-structured problems encountered outside of school. Little is known, beyond anecdotal evidence, about how teachers' consideration of distributions as evidence in well-structured settings compares with their use in ill-structured problem contexts. A qualitative study of preservice secondary teachers examined their use of distributions as evidence in four tasks of varying complexity and ill-structuredness. Results suggest that teachers' incorporation of distributions in well-structured settings does not imply that they will be incorporated in less structured problems (and vice-versa). Implications for research and teaching are discussed.

Changing student teachers' attitudes towards disability and inclusion

A total of 274 preservice teacher education students were surveyed at the beginning and end of a one-semester unit on Human Development and Education which combined formal instruction with structured fieldwork experiences. The latter included interviewing community members regarding their knowledge of Down syndrome and opinions on inclusive education, and writing an associated report. At the end of semester, not only had student teachers acquired more accurate knowledge of Down syndrome, together with more positive attitudes towards the inclusive education of children with Down syndrome, but their attitudes towards disability in general had also changed, and they reported greater ease when interacting with people with disabilities. The study illustrated the value of combining information-based instruction with structured fieldwork experiences in changing attitudes towards disability and inclusion. It also demonstrated that raising awareness of one disability may lead to changes in attitudes towards disability in general.

Ten Australian elementary teachers' discourse and reported pedagogical practices during cooperative learning

This article describes the types of discourse 10 Australian grade 4-6 teachers used after they had been trained to embed cooperative learning in their curriculum and to use communication skills to promote students' thinking and to scaffold their learning. One audiotaped classroom social science lesson involving cooperative learning was analyzed for each teacher. We provide vignettes from 2 teachers as they worked with groups and from 2 student groups. The data from the audiotapes showed that the teachers used a range of mediated-learning behaviors in their interactions with the children that included challenging their perspectives, asking more cognitive and metacognitive questions, and scaffolding their learning. In turn, in their interactions with each other, the children modelled many of the types of discourse they heard their teachers use. Follow-up interviews with the teachers revealed that they believed it was important to set expectations for children's group behaviors, teach the social skills students needed to deal with disagreement in groups, and establish group structures so children understood what was required both from each other and the task. The teachers reported that mixed ability and gender groups worked best and that groups should be no larger than 5 students. All teachers' programs were based on a child-centered philosophy that recognized the importance of constructivist approaches to learning and the key role interaction plays in promoting social reasoning and learning.